iPad Pro update will not move past estimating time remaining

That is a big jump in OS. Are you trying to do this "over the air" or when connected to a computer running iTunes? The latter is far more reliable, especially when one lets the iPadOS get so far behind.

Whether or not you are able to update any iPad to a newer version of iOS/iPadOS will be dictated by the iPad model - and the currently installed version of iOS. You can find this information here:

Settings > General > About

Not sure which iPad you have? Identify your iPad model.

Here is a list of the highest version of iOS supported by the older models of iPad (for simplicity - “generations” are shortened to a number) that are restricted in their ability to be updated:

iPad1 - iOS 5.1.1

iPad2, iPad3 and iPad mini1 - iOS 9.3.5 (WiFi Only models), iOS 9.3.6 (WiFi & Cellular)

iPad4 - iOS 10.3.3 (WiFi Only), iOS 10.3.4 (WiFi & Cellular)

iPad Air1, iPad mini2 and iPad mini3 - iOS 12.5.6

Newer models, not appearing in this list, are all able to be updated to the current version, iPadOS 15.6.1

If your iPad is capable of being updated to a more recent version of iOS/iPadOS than is currently installed, these support pages outline both the available methods by which the update can be performed - and troubleshooting should you experience difficulties:

Update your iPhone, iPad or iPod touch – Apple Support

If you can't update or restore your iPhone, iPad or iPod touch – Apple Support

If your iPhone, iPad or iPod touch won’t update - Apple Support

iOS update and restore errors – Apple Support

Be aware that your iPad may be too far behind the current version to be updated directly from iPad settings. As such, you will likely need to use a computer to perform the update. You will need access to either a PC (with iTunes installed) or a Mac (with iTunes or Finder - as appropriate for the installed version of MacOS). Ensure that your installed version of iTunes has been updated to the most recent version; the essential device drivers are included.

Download and use iTunes for Windows – Apple Support

Update to the latest version of iTunes – Apple Support

Update software on iPhone, iPad or iPod touch in iTunes on PC - Apple Support

You should note that for your iPad to install an available update, its battery must be charged to at least 50% capacity - and/or be connected to its Power Adapter. Similarly, the iPad can only be updated over a standard WiFi connection - or be updated by a PC or Mac using iTunes or Finder - over a USB connection.

There are known issues with update of some iPad models (e.g., iPad Pro 10.5) to iPadOS 15.x. Do you have a WiFi Only, or WiFi+Cellular model of iPad?

For affected WiFi+Cellular models of iPad, many are reporting that removal of the SIM tray from the iPad will allow the verification and installation processes to successfully compete. Other reports suggest that installing a SIM card (whether active or not) also permits the update process to complete.

You may need to restart the update process, but removing the SIM tray from the iPad is simple and costs nothing to try.

Remove or switch the SIM card in your iPhone - Apple Support

If you have a WiFi Only model, the current workaround is to remove the iPad Passcode - and then re-try the installation process. This has also been observed to resolve issues with installing/verifying the update on WiFi+Cellular models.

Be aware that removing the iPad Passcode has implications for any payment methods registered for ApplePay from iPad - and your Keychain (that includes your saved passwords). Assuming that you have other devices (such as an iPhone), your Keychain will remain preserved in iCloud - and can be easily re-synchronised with your iPad via iCloud. Payment cards registered for ApplePay will need to be manually re-added after the update.